A bi-fidelity Asymptotic-Preserving Neural Network approach for multiscale kinetic problems

In this talk, we will introduce a bi-fidelity Asymptotic-Preserving Neural Network (BI-APNNs) framework, designed to efficiently solve forward and inverse problems for the linear Boltzmann equation. Our approach builds upon the previously studied Asymptotic-Preserving Neural Network (APNNs), which employs a micro-macro decomposition to handle the model’s multiscale nature. We specifically address a bottleneck in the original APNNs: the slow convergence of the macroscopic density in the near fluid-dynamic regime. This strategy significantly accelerates the training convergence as well as improves the accuracy of the forward problem solution, particularly in the fluid-dynamic limit. We show several numerical experiments on both linear Boltzmann and the Boltzmann-Poisson system that this new BI-APNN method produces more accurate and robust results for forward and inverse problems compared to the standard APNNs. This is a joint work with Zhenyi Zhu and Xueyu Zhu.